The Federation Starfleet Starship USS Enterprise is sent to the Hekaras Corridor, the only safe path through the sector, to investigate the disappearance of the medical ship U.S.S. Fleming. In the process they find a Ferengi ship, which is badly disabled. The Ferengi daimon contends a Federation buoy disabled his ship.
The Enterprise crew learns a Hekaran brother and sister, Rabal and Serova, are responsible for disabling the ships by using disguised ship-disabling mines. These siblings contend that sustained warp drive is destroying the fabric of space near their homeworld, and will eventually destroy their planet. Data determines that the research has merit, but requires more study. Picard requests a more thorough investigation from the Federation's Science Council.
However, Serova is not willing to wait for any more studies. In order to prove her theory she causes a warp breach in her ship, killing herself in the process. A rift is formed, and the Fleming becomes trapped in the damaged space. The Enterprise crew manages to find a way to "surf" through the rift without using warp drive, beam up the Fleming crew, and escape the rift.
Later, the Federation Council issues a new directive limiting all Federation vessels to a speed of warp five except in extreme emergency. The Klingon Empire also agrees to the limitations, but there is uncertainty as to whether or not the Romulan Star Empire, Ferengi Alliance and Cardassian Union will, as well.
This episode also features much dialogue between Geordi and Data concerning Data's cat, Spot. Geordi had a terrible experience babysitting it, and insists Spot needs training. Data tries multiple techniques, but is unsuccessful.